Let {X,} be an independent Bernoulli sequence with parameter p, and let np, A < o as n oo. Verify directly that the Lindeberg condition fails for {X„}.

Q: 18. Which of these sequences is/are not bounded? I. a, = (-1)", n> 1 А. II only В. I only С. П only.…

A: Option (C) is correct. II only.

Q: 12. Suppose (an) is a Cauchy sequence, and that (bn) is a sequence satisfying lim,co lan - bn| = 0.…

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Q: 30. а, 2 1+ %3D - n

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Q: Find the explicit formula of the following sequence. 8 (72, 24, 8, 3, ...} O a O b Oc - Od ƒ(n) = a₁…

A: Given sequence is 72, 24, 8, 83, ...

Q: 16. Show that if (s} and (ta} Cauchy sequence. Cauchy sequences, then {s + tn} is also are a.

A: Consider the provided question, We have to show that if {sn} and {tn} are Cauchy sequence then {sn +…

Q: 5. Consider the sequence {an}. Defined by the recurrence relation; a₁ = 1, an+1 = (2an+3), for n ≥…

A: We have to prove the sequence is increasing bounded above by

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Q: Let {an} and {bn} be two Cauchy sequences of real numbers. Then show that the sequence {|an − bn|}…

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Q: Prove that x ∈ E' iff there exists a sequence (xn) in E\{x} such that xn -> x.

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Q: 50. A sequence a, is defined inductively as a, = v3 and a41 = /3 + a, ,Vn 2 1. Find the limit %3D of…

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Q: nat if xn and yn Cauchy sequence, then xn >

A: A sequence is {a} is called Cauchy sequence if for ∈&gt;0 there exists N such that m, n&gt;N then…

Q: 1- if (x,) Chauchy sequence show that (x,) bounded.

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Q: Suppose that (0) is a null sequence with only nonzero terms. Calculate lim 818 0 Submit Question sin…

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Q: 2. 0.03 of the goods produced in a factory are defective. When a 25 unit sample is drawn for…

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Q: Find the recurrence relation and the initial condition for the following sequence     242,80,26,8,2…

A: Solution: The objective is to find the recurrence relation and the initial condition for the…

Q: Suppose {f,} is a sequence in Banach space B s.t. ||fn - fn+1|| s'/2-). Show that the sequence {f,}…

A: For a vector space X, over a field F, a normed linear space X,· is referred to as Banach space if…

Q: A momotone sequence converges if and only if it is bounded ylgn İhi

A: True

Q: Let {an} be a monotone sequence. Show that (a,} is a Cauchy sequence if and only if it is bounded.

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Q: 2. Let an be the sequence defined inductively by ai = 2 and an+1 = 1 an + 2 an (a) Prove by…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three sub…

Q: 2) The purpose of this problem is to give you some practice with the most common application of The…

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Q: 13. Let (an)=I be a Cauchy sequence, and let p : N → N be a one-to-one function. Show that the…

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Q: Let {n} be a Cauchy sequence. Prove that {s} is bounded.

A: Given: In this question, the given details are, Let {sn} be a Cauchy sequence. To Prove that {sn} is…

Q: Aşağıdaki dizilerden hangisi “ yakınsak, azalan ve en küçük üst sının 1" olan bir dizidir? b) {an}=…

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Q: (b) Let (an) and (b) be Cauchy sequences. Prove from first principles that their (an + bn) is a…

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Q: A sequence a, is defined inductively as a1 of an if an < an +1 Vn 2 1. A.글 (1± v13) B. (1– V13) C.…

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Q: Use the definition to prove that {(-

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Q: Assume that a person invests $2000 each year in a tax-sheltered annuity at 10% interest compounded…

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Q: Suppose that {a;} is a Cauchy sequence in a metric space X, d and lim an = p. Suppose, in addition,…

A: We have to prove that limn→∞bn=p Given that ai is a Cauchy sequence. Let ε&gt;0 then ∃N1∈N such that…

Q: 1. Let a, = 1 and an+1 = 1+ 1+an (a) Find the first six terms of the sequence {an}. (b) Prove that…

A: As you asked multiple sub parts so I answered 1st three subpart.

Q: Prove that az E E' iff there exists a sequence (en) in E\{x} such that xnx.

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Q: Suppose f: D→ R with ao the only accumulation point of D. If {an}1 is a Cauchy sequence with an ED…

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Q: Suppose {xn} is a bounded sequence. Define bn where lim inf xn :_(n→∞) = lim inf bn :_(n→∞). Show…

A: It is given that xn is the bounded sequence. bn:=infxk: k⩾n Wherelimn→∞infxn:=limn→∞bn To prove bn…